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Congestion problems are increasing in number in power transmission networks due to the increment of renewable power sources along it. To reduce their impact, Transmission System Operators (TSOs) as the French RTE use network reconfiguration or renewable power curtailment in complex subtransmission areas. The operators need enhanced methodological tools to better address the optimal power flow management problem by also using novel levers as for example the storage devices. This paper proposes mathematical models which integrate the possibility to partially curtail the renewable power in the form of a dynamical system representing the transmission network, also considering storage devices.

Optimal Power Flow (OPF) can be modeled as a nonconvex Quadratically Constrained Quadratic Program (QCQP). Our purpose is to solve OPF to global optimality. To this end, we specialize the Mixed-Integer Quadratic Convex Reformulation method (MIQCR) to (OPF). This is a method in two steps. First, a Semi-Definite Programming (SDP) relaxation of (OPF) is solved. Then the optimal dual variables of this relaxation are used to reformulate OPF into an equivalent new quadratic program, where all the non-convexity is moved to one additional constraint. In the second step, this reformulation is solved within a branch-and-bound algorithm, where at each node a quadratic and convex relaxation of the reformulated problem, obtained by relaxing the non-convex added constraint, is solved. The key point of our approach is that the lower bound at the root node of the branch-and-bound tree is equal to the SDP relaxation value.We test this method on several OPF cases, from two-bus networks to more-than-a-thousand-buses networks from the MAT-POWER repository. Our first results are very encouraging.

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